Field of the Invention
This invention relates to 3-D polarimetric imaging, and more particular to a method of generating the surface normal calibration maps φ(AoLP) and θ(DoLP,φ) to compensate for structured scene reflections.
Description of the Related Art
Imaging detectors, such as focal plane arrays (FPAs), generally include an array of pixels, each pixel including a photo-detector that generates a signal responsive to light generated or reflected by an object. These signals are collected and combined such that a 2-D digital image of the object can be created. Pixelated filter arrays positioned in a fixed location over the detector array are widely used in commercial imaging systems to provide hyperspectral capability. For example, digital cameras use fixed-in-place pixelated filter arrays for color (RGB) photography. These filters reduce the amount of light that reaches the imaging pixel (for example, a red filter reflects blue and green light). For example a 2×2 filter sub-array of R/G/G/B maps to a 2×2 grouping of detector pixels that form a single image pixel.
A polarimetric digital camera may use a Linear Stokes Polarimeter to analyze the polarization components of light to, for example, extract shape information from an object. Polarimetry requires at least three measurements to analyze the polarization components of light; at least two different polarization components and possibly an unpolarized component. The Linear Stokes Polarimeter may output directly or electronics may compute an Angle of Linear Polarization (AoLP) image and a Degree of Linear Polarization (DoLP) image from the measurements to extract 2-D shape information.
One embodiment of a Linear Stokes Polarimeter is a rotating linear polarizer that time multiplexes the at least three measurements taken at different times, hence different angular values. Another embodiment is a pixelated filter array in which the filter sub-arrays have different linear polarizations. Typically, the pixelated filter array, and detector, are divided into groups of four pixels (e.g., a 2×2 sub-array of pixels) that form a single image pixel. The standard commercially available polarized pixelated filter sub-array is a 2×2 array of linear polarizers having angular values of Θ1=0°, Θ2=45°, Θ3=90° and Θ4=135°, respectively, which are optimum assuming perfect alignment between the pixelated filter array and the FPA. U.S. Patent Publication 2014/0063299 to Fest et. al. entitled “Movable Pixelated Filter Array” describes a technique for using the data reduction matrix to account for misalignment.
The AoLP and DoLP images can be processed to extract 3-D shape information and form a 3-D image of the object. Surface normal calibration maps φ(AoLP) and θ(DoLP,φ) map the values of the respective images to the azimuth angle φ and elevation angle θ that together define the surface normal at a given location on the object. These maps are computed based on idealized plots 10 and 12 of specular s-polarized and p-polarized reflectance, respectively, versus angle of incidence for a given surface (e.g. smooth aluminum at 3 microns) as shown in FIG. 1. A DoLP 14 is computed as (S−P/S+P). The maps are used to compute the surface normal at points on the target. A shape shading algorithm such as the Frankot-Chellapa algorithm (see Robert T. Frankot and Rama Chellappa, “A Method for Enforcing Integrability in Shape from Shading Algorithms” IEEE Trans. on Pattern Analysis and machine Intelligence, Vol. 40, No. 4, July 1988), which is hereby incorporated by reference, processes the surface normal to compute a depth at each pixel, which together with the surface normal forms the 3-D image of the object.
Sensors operating in the VIS, NIR, or SWIR wavebands can only see room temperature targets if the targets are illuminated by external sources (such as the sun or a light) and the reflected light hits the sensor. For this reason, these bands are often called “reflective bands”. The Fresnel equations predict that this reflected light is s-polarized; that is, the orientation of linear polarization of the light reflected from the target is perpendicular to the plane containing the surface normal and the Line of Sight (LOS) vector (aka the scatter plane). The degree of s-polarization is determined by surface properties of the object such as the orientation of the surface, its complex refractive index, and its roughness. Sensors operating in the MWIR and LWIR see a combination of light emitted from the room-temperature target and light that is reflected from the target by sources around it. These bands are called “emissive bands”, and light emitted from a target is p-polarized (orientation of polarization is parallel to the scatter plane). Light reflected from the target is polarized perpendicular to the emitted light, and therefore will cancel out some (or all) of the polarization. The degree of p-polarization is determined by the surface properties of the object.
Daisuke Miyazaki et. al., “Determining surface orientations of transparent objects based on polarization degrees in visible and infrared wavelengths” Vol. 19, No. 4, April 2002, J. Opt. Soc. Am. A discloses a method for obtaining surface orientations of transparent surfaces through analysis of the degree of polarization in surface reflection and emission in visible and far-infrared wavelengths, respectively. The degree of polarization at visible wavelengths provides two possible surface orientations. The polarization degree in the infrared wavelengths is used to disambiguate the results and select the single surface orientation. Miyazaki employs a spherical diffuser illuminated from point light sources as the external source for the visible light measurements to illuminate an object located at the center of the diffuser from all directions. Miyazaki heats the object to 30-40° and assumes that the infrared light is dominated by emissions, an additional light source is not used. Miyazaki constructs his measurements in such a way to avoid structured scene reflections from multiple external sources such that the different calibration maps for the visible and IR bands can be derived from FIG. 1.
Another class of 3-D polarimetric imaging techniques attempts to compensate for structured scene reflections from multiple external sources in the band of interest. If uncompensated, the structured scene reflections can introduce a bias in the calibration maps that corrupts the 3-D image. Given a radiance map (location, size and brightness of light sources) of a known environment, these techniques assume that the measured reflectance from each object pixel is a combination of a specular component and a diffuse component. The specular component is s-polarized. The techniques identify the pixels that are strongly s-polarized (specular) and use mappings derived from FIG. 1 to identify the elevation angle. Only pixels that are strongly s-polarized are processed. Therefore, a given source will only produce the calibration map over a narrow angular range. This approach requires multiple sources at different locations to adequately populate the calibration maps. Furthermore, the accuracy of the calibration maps is limited by the assumption that each object pixel is a combination of a specular component and a diffuse component. U.S. Pat. Nos. 5,028,138; 7,737,975 and 7,948,514 disclose variants of this based on the same specular/diffuse assumption.